Forward Exchange Rates

  8. Forward Exchange Rate
 Definition  Forward exchange markets deal in promises to sell or buy foreign exchange at a specified rate, and at a specified time in the future with payment to be made upon delivery. These promises are known as forward exchange and the price is the forward exchange rate. Forward exchange markets do not operate during periods of hyperinflation.

The forward exchange market resembles the futures markets found in organized commodity markets, such as wheat and coffee. The primary function of forward market is to afford protection against the risk of fluctuations in exchange rates.

 when forward markets are active Forward markets are most useful

(i) under flexible exchange rate system and if there are significant exchange variations,

(ii) under fixed exchange rate system, if there is a strong possibility of devaluation/revaluation,

Non operational 

(i) it cannot function when exchange control is imposed.

(ii) it cannot function during periods of hyperinflation.


  9. Interest Rate Parity Theory (Keynes)
 What is IRPT?

 It is John Maynard Keynes' theory of how forward rates are determined.

When short term interests are higher in one market than in another, investors will be motivated to shift funds between markets, say New York and London.

Investors borrow (or buy) a low interest currency and lend the same amount in a high interest currency. This is called carry trade. There is roughly a 5% difference in the interest rates between Japan and the US. To make profits from differeing interest rates, investors must convert, for example, dollars (a low interest currency) into pound sterling (a high interest currency) for investment in London. However, they would be exposed to an exchange risk. If the exchange rate is stable, the investors gain the interest differential, (i - i*), by shifting funds from New York to London.

          If pound appreciates during the investment period, the foreign investors will reap additional gain in the change in the exchange rate. However, if pound depreciates, they will experience an exchange loss. The exchange loss may partially or more than offset the gain in the interest income.

          To avoid this exchange loss, dollar investors want cover against the exchange loss by selling pound forward. The amount of forward pound to sell is equal to the purchase of spot pound plus the interest earned in London. This practice is called interest arbitrage. Interest arbitrage links the two national money markets and the forward market.

 Example  Assume: a US investor has A dollars to invest, either in New York or in London. The annual interests in the US and the UK are 8% and 12%, respectively. The quarterly interest rates in the US and UK are then 2% and 3%, respectively.
 Do nothing (take risk) (1) Invest in New York for 90 days.

$1M(1 + .02) = $1.02M

(2) Invest in London

£t=0 = $1M/spot = $1M/1.5 = £666,667.

If St=90 = St=0, then investing overseas is better ($10,000 more return).

If St=90 = 1.65 (£ rose 10%), then

$10,000 (interest gain) + $103,000 (appreciation of £) = $113,000 (foreign investment is definitely better).

If St=90 = 1.35 (£ fell 10%), then

$10,000 (interest gain) - $103,000 (depreciation of £) = - $93,000.

Most investors would rather avoid this exchange risk.



  10. How to avoid foreign exchange risk
 Enter Forward market  You may enter the forward exchange market. As long as the return from overseas investment is greater than the domestic return, one would sell forward pound (or whichever currency in question). Only when the forward transactions are made, the risk can be avoided. However, avoiding the foreign exchange risk may be too costly, in which case it is not profitable to avoid the risk.

(i) If F = $1.47, then

St=90 = 686.667 x 1.47 < 1.02 million. You are worse off.

Even if i* > i, do not invest in the UK. (That is, taking the foreign exchange risk is cheaper)

(ii) If F = $1.53, then

St=90 = 686.667 x 1.53 >1.02 million. You are better off.

Invest in the UK. (In this case, forward transactions are profitable and eliminate the foreign exchange risk.)

 Investing in NY If one invested A dollars in New York, then at the end of 90 days, the return will be

(1) A(1 + i)

i = i90 = annual interest rate ÷ 4.

However, the subscript 90 is suppressed (too cumbersome)

 Investing in London If one invested in London (by buying pounds in the spot market, and selling pound forward, the investor can cover against the exchange risk (interest arbitrage)

(2) A(1 + i*)(F/S)

F = price of one pound sterlilng for delivery 90 days hence

S = price of one pound sterling in the spot market

 Equilibrium forward rate? Interest arbitrarage will cause the forward rate to adjust to the interest rate differential until it reaches an equilibrium rate. This equilibrium rate F is determined by

(3) A(1 + i) = A (1 + i*)(F/S).

Solve for F.

(4) F = S(1 + i)/(1 + i*).

Since i and i* are small fractions, this is approximately equal to:

F = S(1 + i - i*), or

i - i* = (F - S)/S.


That is, if the domestic interest rate is higher, the forward pound must be sold at a premium. Specifically, the domestic interest advantage (i - i*) must be equal to %premium on the forward pound when the forward rate is at its parity.

For example, if the domestic interest is 1% above the foreign interest rate, forward pound must be higher than the spot rate by the same proportion to prevent capital flows.



  11. Covered Arbitrage Margin
 Covered arbitrage margin  (CAM) = (i - i*) - (F - S)/S.
 When capital inflow

 If i - i* > (F - S)/S, then K* inflow occurs.

(Domestic investors have no incentive to invest abroad, but foreign investors will invest in America)

When capital outflow occurs   

If i - i* < (F - S)/S, then K outflow occurs. (Foreign investors will stay put, but domestic investors will move funds abroad)

  Remark: If i = i*, there is no incentive for any investors to move funds between countries, except for the forward premium. In this case, if F > S, domestic investors would make money by selling forward currency and invest abroad. As a matter of fact, if the forward premium is sufficiently large and more than offset the possible interest loss (i - i* > 0), one could invest overseas.

If i - i* = (F - S)/S, then no capital flow.

 Interest parity Let Fo be the rate at which no capital flow occurs. If F = Fo, then the forward rate is at its interest parity.

Federal Reserve Bulletin publishes CAM, e, i, i*. CAM are very nearly zero.

 Interest rate parity  

Problems of IRP Theory

Keynes' theory does not take into account differing investment risks between the two countries.

(1) Interest rates in developing and transition economies are generally higher, due to higher risks.

(2) Inflation rates also differ between countries. It is not the nominal payoffs, but real interest rates. Thus, different inflation rates will affect investment decisions.


Currencies of the World, Pacific Exchange Rate Service